where \(\alpha _1,\alpha _2 > 0\)  are the user-selected step size and \(P_{\mathcal {Y}}(y)\)  denotes the projection operator [1]} that projects \(y\)  onto the set \(\mathcal {Y}\) . The key is to obtain the partial derivatives \(\partial J^* / \partial \xi \)  and \(\partial J^* / \partial T\) , which stand for the sensitivity of the optimal cost of (REF ) to \(\xi \)  and \(T\) , respectively. We use OptNet [2]} to obtain these two gradients. Specifically, the OptNet allows computing the analytical gradient of the optimal cost with respect to the coefficients of a QP (e.g., \(P(T)\) , \(q(T)\) , \(C(T)\) , \(A(T)\) , \(\xi \) , and \(b\)  in (REF )) by implicitly differentiating the KKT condition. Using the method enabled by OptNet, we can directly obtain
\(\frac{\partial J^*}{\partial \xi }, \frac{\partial J^*}{\partial P(T)}, \frac{\partial J^*}{\partial q(T)}, \frac{\partial J^*}{\partial C(T)}, \frac{\partial J^*}{\partial A(T)}.\) 
